Page 1 You must have observed your teacher recording the attendance of students in your class everyday, or recording marks obtained by you after every test or examination. Similarly, you must have also seen a cricket score board. Two score boards have been illustrated here : You know that in a game of cricket the information recorded is not simply about who won and who lost. In the score board, you will also find some equally important information about the game. For instance, you may find out the time taken and number of balls faced by the highest run-scorer. Name of the bowlers Overs Maiden overs Runs given Wickets taken A 10 2 40 3 B 10 1 30 2 C 10 2 20 1 D 10 1 50 4 Name of the batsmen Runs Balls faced Time (in min.) E 45 62 75 F 55 70 81 G 37 53 67 H 22 41 55 9.1 Introduction Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9 Data Handling Data Handling Data Handling Data Handling Data Handling 2020-21 Page 2 You must have observed your teacher recording the attendance of students in your class everyday, or recording marks obtained by you after every test or examination. Similarly, you must have also seen a cricket score board. Two score boards have been illustrated here : You know that in a game of cricket the information recorded is not simply about who won and who lost. In the score board, you will also find some equally important information about the game. For instance, you may find out the time taken and number of balls faced by the highest run-scorer. Name of the bowlers Overs Maiden overs Runs given Wickets taken A 10 2 40 3 B 10 1 30 2 C 10 2 20 1 D 10 1 50 4 Name of the batsmen Runs Balls faced Time (in min.) E 45 62 75 F 55 70 81 G 37 53 67 H 22 41 55 9.1 Introduction Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9 Data Handling Data Handling Data Handling Data Handling Data Handling 2020-21 DATA HANDLING 185 Similarly, in your day to day life, you must have seen several kinds of tables consisting of numbers, figures, names etc. These tables provide ‘Data’. A data is a collection of numbers gathered to give some information. 9.2 Recording Data Let us take an example of a class which is preparing to go for a picnic. The teacher asked the students to give their choice of fruits out of banana, apple, orange or guava. Uma is asked to prepare the list. She prepared a list of all the children and wrote the choice of fruit against each name. This list would help the teacher to distribute fruits according to the choice. Raghav — Banana Bhawana — Apple Preeti — Apple Manoj — Banana Amar — Guava Donald — Apple Fatima — Orange Maria — Banana Amita — Apple Uma — Orange Raman — Banana Akhtar — Guava Radha — Orange Ritu — Apple Farida — Guava Salma — Banana Anuradha — Banana Kavita — Guava Rati — Banana Javed — Banana If the teacher wants to know the number of bananas required for the class, she has to read the names in the list one by one and count the total number of bananas required. To know the number of apples, guavas and oranges separately she has to repeat the same process for each of these fruits. How tedious and time consuming it is! It might become more tedious if the list has, say, 50 students. So, Uma writes only the names of these fruits one by one like, banana, apple, guava, orange, apple, banana, orange, guava, banana, banana, apple, banana, apple, banana, orange, guava, apple, banana, guava, banana. Do you think this makes the teacher’s work easier? She still has to count the fruits in the list one by one as she did earlier. Salma has another idea. She makes four squares on the floor. Every square is kept for fruit of one kind only. She asks the students to put one pebble in the square which matches their Banana Orange Apple 2020-21 Page 3 You must have observed your teacher recording the attendance of students in your class everyday, or recording marks obtained by you after every test or examination. Similarly, you must have also seen a cricket score board. Two score boards have been illustrated here : You know that in a game of cricket the information recorded is not simply about who won and who lost. In the score board, you will also find some equally important information about the game. For instance, you may find out the time taken and number of balls faced by the highest run-scorer. Name of the bowlers Overs Maiden overs Runs given Wickets taken A 10 2 40 3 B 10 1 30 2 C 10 2 20 1 D 10 1 50 4 Name of the batsmen Runs Balls faced Time (in min.) E 45 62 75 F 55 70 81 G 37 53 67 H 22 41 55 9.1 Introduction Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9 Data Handling Data Handling Data Handling Data Handling Data Handling 2020-21 DATA HANDLING 185 Similarly, in your day to day life, you must have seen several kinds of tables consisting of numbers, figures, names etc. These tables provide ‘Data’. A data is a collection of numbers gathered to give some information. 9.2 Recording Data Let us take an example of a class which is preparing to go for a picnic. The teacher asked the students to give their choice of fruits out of banana, apple, orange or guava. Uma is asked to prepare the list. She prepared a list of all the children and wrote the choice of fruit against each name. This list would help the teacher to distribute fruits according to the choice. Raghav — Banana Bhawana — Apple Preeti — Apple Manoj — Banana Amar — Guava Donald — Apple Fatima — Orange Maria — Banana Amita — Apple Uma — Orange Raman — Banana Akhtar — Guava Radha — Orange Ritu — Apple Farida — Guava Salma — Banana Anuradha — Banana Kavita — Guava Rati — Banana Javed — Banana If the teacher wants to know the number of bananas required for the class, she has to read the names in the list one by one and count the total number of bananas required. To know the number of apples, guavas and oranges separately she has to repeat the same process for each of these fruits. How tedious and time consuming it is! It might become more tedious if the list has, say, 50 students. So, Uma writes only the names of these fruits one by one like, banana, apple, guava, orange, apple, banana, orange, guava, banana, banana, apple, banana, apple, banana, orange, guava, apple, banana, guava, banana. Do you think this makes the teacher’s work easier? She still has to count the fruits in the list one by one as she did earlier. Salma has another idea. She makes four squares on the floor. Every square is kept for fruit of one kind only. She asks the students to put one pebble in the square which matches their Banana Orange Apple 2020-21 MATHEMATICS 186 choices. i.e. a student opting for banana will put a pebble in the square marked for banana and so on. By counting the pebbles in each square, Salma can quickly tell the number of each kind of fruit required. She can get the required information quickly by systematically placing the pebbles in different squares. Try to perform this activity for 40 students and with names of any four fruits. Instead of pebbles you can also use bottle caps or some other tokens. 9.3 Organisation of Data To get the same information which Salma got, Ronald needs only a pen and a paper. He does not need pebbles. He also does not ask students to come and place the pebbles. He prepares the following table. Do you understand Ronald’s table? What does one (3) mark indicate? Four students preferred guava. How many (3) marks are there against guava? How many students were there in the class? Find all this information. Discuss about these methods. Which is the best? Why? Which method is more useful when information from a much larger data is required? Example 1 : A teacher wants to know the choice of food of each student as part of the mid-day meal programme. The teacher assigns the task of collecting this information to Maria. Maria does so using a paper and a pencil. After arranging the choices in a column, she puts against a choice of food one ( | ) mark for every student making that choice. Banana 3 3 3 3 3 3 3 3 8 Orange 3 3 3 3 Apple 3 3 3 3 3 5 Guava 3 3 3 3 4 Choice Number of students Rice only | | | | | | | | | | | | | | | | | Chapati only | | | | | | | | | | | | | Both rice and chapati | | | | | | | | | | | | | | | | | | | | Guava 2020-21 Page 4 You must have observed your teacher recording the attendance of students in your class everyday, or recording marks obtained by you after every test or examination. Similarly, you must have also seen a cricket score board. Two score boards have been illustrated here : You know that in a game of cricket the information recorded is not simply about who won and who lost. In the score board, you will also find some equally important information about the game. For instance, you may find out the time taken and number of balls faced by the highest run-scorer. Name of the bowlers Overs Maiden overs Runs given Wickets taken A 10 2 40 3 B 10 1 30 2 C 10 2 20 1 D 10 1 50 4 Name of the batsmen Runs Balls faced Time (in min.) E 45 62 75 F 55 70 81 G 37 53 67 H 22 41 55 9.1 Introduction Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9 Data Handling Data Handling Data Handling Data Handling Data Handling 2020-21 DATA HANDLING 185 Similarly, in your day to day life, you must have seen several kinds of tables consisting of numbers, figures, names etc. These tables provide ‘Data’. A data is a collection of numbers gathered to give some information. 9.2 Recording Data Let us take an example of a class which is preparing to go for a picnic. The teacher asked the students to give their choice of fruits out of banana, apple, orange or guava. Uma is asked to prepare the list. She prepared a list of all the children and wrote the choice of fruit against each name. This list would help the teacher to distribute fruits according to the choice. Raghav — Banana Bhawana — Apple Preeti — Apple Manoj — Banana Amar — Guava Donald — Apple Fatima — Orange Maria — Banana Amita — Apple Uma — Orange Raman — Banana Akhtar — Guava Radha — Orange Ritu — Apple Farida — Guava Salma — Banana Anuradha — Banana Kavita — Guava Rati — Banana Javed — Banana If the teacher wants to know the number of bananas required for the class, she has to read the names in the list one by one and count the total number of bananas required. To know the number of apples, guavas and oranges separately she has to repeat the same process for each of these fruits. How tedious and time consuming it is! It might become more tedious if the list has, say, 50 students. So, Uma writes only the names of these fruits one by one like, banana, apple, guava, orange, apple, banana, orange, guava, banana, banana, apple, banana, apple, banana, orange, guava, apple, banana, guava, banana. Do you think this makes the teacher’s work easier? She still has to count the fruits in the list one by one as she did earlier. Salma has another idea. She makes four squares on the floor. Every square is kept for fruit of one kind only. She asks the students to put one pebble in the square which matches their Banana Orange Apple 2020-21 MATHEMATICS 186 choices. i.e. a student opting for banana will put a pebble in the square marked for banana and so on. By counting the pebbles in each square, Salma can quickly tell the number of each kind of fruit required. She can get the required information quickly by systematically placing the pebbles in different squares. Try to perform this activity for 40 students and with names of any four fruits. Instead of pebbles you can also use bottle caps or some other tokens. 9.3 Organisation of Data To get the same information which Salma got, Ronald needs only a pen and a paper. He does not need pebbles. He also does not ask students to come and place the pebbles. He prepares the following table. Do you understand Ronald’s table? What does one (3) mark indicate? Four students preferred guava. How many (3) marks are there against guava? How many students were there in the class? Find all this information. Discuss about these methods. Which is the best? Why? Which method is more useful when information from a much larger data is required? Example 1 : A teacher wants to know the choice of food of each student as part of the mid-day meal programme. The teacher assigns the task of collecting this information to Maria. Maria does so using a paper and a pencil. After arranging the choices in a column, she puts against a choice of food one ( | ) mark for every student making that choice. Banana 3 3 3 3 3 3 3 3 8 Orange 3 3 3 3 Apple 3 3 3 3 3 5 Guava 3 3 3 3 4 Choice Number of students Rice only | | | | | | | | | | | | | | | | | Chapati only | | | | | | | | | | | | | Both rice and chapati | | | | | | | | | | | | | | | | | | | | Guava 2020-21 DATA HANDLING 187 Umesh, after seeing the table suggested a better method to count the students. He asked Maria to organise the marks ( | ) in a group of ten as shown below : Rajan made it simpler by asking her to make groups of five instead of ten, as shown below : Teacher suggested that the fifth mark in a group of five marks should be used as a cross, as shown by ‘ ’. These are tally marks. Thus, shows the count to be five plus two (i.e. seven) and shows five plus five (i.e. ten). With this, the table looks like : Choice T ally marks Number of students Rice only 17 Chapati only 13 Both rice and chapati 20 Example 2 : Ekta is asked to collect data for size of shoes of students in her Class VI. Her finding are recorded in the manner shown below : 5 4 7 5 6 7 6 5 6 6 5 4 5 6 8 7 4 6 5 6 4 6 5 7 6 7 5 7 6 4 8 7 Choice T ally marks Number of students Rice only | | | | | | | | | | | | | | | | | 17 Chapati only | | | | | | | | | | | | | 13 Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20 Choice T ally marks Number of students Rice only | | | | | | | | | | | | | | | | | 17 Chapati only | | | | | | | | | | | | | 13 Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20 2020-21 Page 5 You must have observed your teacher recording the attendance of students in your class everyday, or recording marks obtained by you after every test or examination. Similarly, you must have also seen a cricket score board. Two score boards have been illustrated here : You know that in a game of cricket the information recorded is not simply about who won and who lost. In the score board, you will also find some equally important information about the game. For instance, you may find out the time taken and number of balls faced by the highest run-scorer. Name of the bowlers Overs Maiden overs Runs given Wickets taken A 10 2 40 3 B 10 1 30 2 C 10 2 20 1 D 10 1 50 4 Name of the batsmen Runs Balls faced Time (in min.) E 45 62 75 F 55 70 81 G 37 53 67 H 22 41 55 9.1 Introduction Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9 Data Handling Data Handling Data Handling Data Handling Data Handling 2020-21 DATA HANDLING 185 Similarly, in your day to day life, you must have seen several kinds of tables consisting of numbers, figures, names etc. These tables provide ‘Data’. A data is a collection of numbers gathered to give some information. 9.2 Recording Data Let us take an example of a class which is preparing to go for a picnic. The teacher asked the students to give their choice of fruits out of banana, apple, orange or guava. Uma is asked to prepare the list. She prepared a list of all the children and wrote the choice of fruit against each name. This list would help the teacher to distribute fruits according to the choice. Raghav — Banana Bhawana — Apple Preeti — Apple Manoj — Banana Amar — Guava Donald — Apple Fatima — Orange Maria — Banana Amita — Apple Uma — Orange Raman — Banana Akhtar — Guava Radha — Orange Ritu — Apple Farida — Guava Salma — Banana Anuradha — Banana Kavita — Guava Rati — Banana Javed — Banana If the teacher wants to know the number of bananas required for the class, she has to read the names in the list one by one and count the total number of bananas required. To know the number of apples, guavas and oranges separately she has to repeat the same process for each of these fruits. How tedious and time consuming it is! It might become more tedious if the list has, say, 50 students. So, Uma writes only the names of these fruits one by one like, banana, apple, guava, orange, apple, banana, orange, guava, banana, banana, apple, banana, apple, banana, orange, guava, apple, banana, guava, banana. Do you think this makes the teacher’s work easier? She still has to count the fruits in the list one by one as she did earlier. Salma has another idea. She makes four squares on the floor. Every square is kept for fruit of one kind only. She asks the students to put one pebble in the square which matches their Banana Orange Apple 2020-21 MATHEMATICS 186 choices. i.e. a student opting for banana will put a pebble in the square marked for banana and so on. By counting the pebbles in each square, Salma can quickly tell the number of each kind of fruit required. She can get the required information quickly by systematically placing the pebbles in different squares. Try to perform this activity for 40 students and with names of any four fruits. Instead of pebbles you can also use bottle caps or some other tokens. 9.3 Organisation of Data To get the same information which Salma got, Ronald needs only a pen and a paper. He does not need pebbles. He also does not ask students to come and place the pebbles. He prepares the following table. Do you understand Ronald’s table? What does one (3) mark indicate? Four students preferred guava. How many (3) marks are there against guava? How many students were there in the class? Find all this information. Discuss about these methods. Which is the best? Why? Which method is more useful when information from a much larger data is required? Example 1 : A teacher wants to know the choice of food of each student as part of the mid-day meal programme. The teacher assigns the task of collecting this information to Maria. Maria does so using a paper and a pencil. After arranging the choices in a column, she puts against a choice of food one ( | ) mark for every student making that choice. Banana 3 3 3 3 3 3 3 3 8 Orange 3 3 3 3 Apple 3 3 3 3 3 5 Guava 3 3 3 3 4 Choice Number of students Rice only | | | | | | | | | | | | | | | | | Chapati only | | | | | | | | | | | | | Both rice and chapati | | | | | | | | | | | | | | | | | | | | Guava 2020-21 DATA HANDLING 187 Umesh, after seeing the table suggested a better method to count the students. He asked Maria to organise the marks ( | ) in a group of ten as shown below : Rajan made it simpler by asking her to make groups of five instead of ten, as shown below : Teacher suggested that the fifth mark in a group of five marks should be used as a cross, as shown by ‘ ’. These are tally marks. Thus, shows the count to be five plus two (i.e. seven) and shows five plus five (i.e. ten). With this, the table looks like : Choice T ally marks Number of students Rice only 17 Chapati only 13 Both rice and chapati 20 Example 2 : Ekta is asked to collect data for size of shoes of students in her Class VI. Her finding are recorded in the manner shown below : 5 4 7 5 6 7 6 5 6 6 5 4 5 6 8 7 4 6 5 6 4 6 5 7 6 7 5 7 6 4 8 7 Choice T ally marks Number of students Rice only | | | | | | | | | | | | | | | | | 17 Chapati only | | | | | | | | | | | | | 13 Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20 Choice T ally marks Number of students Rice only | | | | | | | | | | | | | | | | | 17 Chapati only | | | | | | | | | | | | | 13 Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20 2020-21 MATHEMATICS 188 Do This Javed wanted to know (i) the size of shoes worn by the maximum number of students. (ii) the size of shoes worn by the minimum number of students. Can you find this information? Ekta prepared a table using tally marks. Shoe size T ally marks Number of students 4 5 5 8 6 10 7 7 8 2 Now the questions asked earlier could be answered easily. You may also do some such activity in your class using tally marks. 1. Collect information regarding the number of family members of your classmates and represent it in the form of a table. Find to which category most students belong. Make a table and enter the data using tally marks. Find the number that appeared (a) the minimum number of times? (b) the maximum number of times? (c) same number of times? Number of family T ally marks Number of students members with that many family members Rows Number of books 9.4 Pictograph A cupboard has five compartments. In each compartment a row of books is arranged. The details are indicated in the adjoining table : 2020-21Read More

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